Saudi Arabia's King Abdullah (centre, seated) has splashed out $36bn in the hope of heading off unrest. Photograph: Ho/Reuters

With Tunisia's Zine El Abidine Ben Ali and Egypt's Hosni Mubarak gone, Muammar Gaddafi teetering on the brink in Libya and Arab leaders everywhere nervously reassessing their survival prospects, there has never been a more auspicious time for people across the region to demand their rights. Even in Saudi Arabia people are stirring.

Their actions are not the sort that attract much attention from the world's media, and especially not the TV cameras, but in a Saudi context they are momentous.

"Unhappiness with the current situation is something that has brought sworn enemies together," writes Eman al-Nafjan, a postgraduate mother of three who blogs under the name Saudiwoman:

"It's becoming more and more difficult to tell apart the demands of conservatives from those of liberals and the demands of the majority from those of minorities … Across the board, there's a demand for a constitutional monarchy and accountability and the end of corruption in handling the nation's wealth."

Taking to the streets and setting fire to police stations may not be the Saudi way of protesting but in the last few days a lot of other things have been happening.

Mohamad al-Deheme, a 24-year-old computer programmer set up a website called shakwa.net (the Arabic word for "grievance") where the public can post complaints directed at government ministries – and already the site has several hundred.

Then there are petitions. One of them, headed "Towards the state of rights and institutions", attracted 1,554 signatures on the internet before the authorities blocked access to it inside the kingdom.

Another came from the "February 23 Youth" group who are demanding "national reform, constitutional reform, national dialogue, elections and female participation".

Yet another, "from Saudi intellectuals to the political leadership", is headed "Declaration of national reform". On Monday, that too was blocked by the Saudi authorities.

The highest-ranking Saudi to join the fray is Prince Alwaleed bin Talal, said to be the world's eighth-richest man, who wrote in the New York Times, calling for "unwavering, enduring and sincere" reform.

To outsiders more accustomed to open dissent, all this petitioning and complaining may look like no big deal. But under an absolute monarchy, even petitioning can get you into serious trouble.

In 2006, Musa al-Qarni and three other men politely asked the king to form an Islamic debating society that would discuss "freedom, justice, equality, citizenship, pluralism, [proper] advice, and the role of women". The king ignored his request and several months later, Qarni was arrested and carted off to jail after the secret police stormed a villa in Jeddah where several men "widely known for their advocacy on issues of social and political reform" were meeting.

The national reform declaration (translated here by Ahmed al-Omran who blogs as Saudi Jeans) is the most detailed of the recent calls for change. It's a very sensible assessment of what needs to be done and its 12 points cover such issues as the rule of law, elections, corruption, independence of the judiciary, women's rights and civil society activity.

King Abdullah, meanwhile, is plainly apprehensive. His response so far has been to dig deep into his – or the state's – pockets (in Saudi Arabia there isn't really much distinction between the two). Since returning from medical treatment abroad he has splashed out $36bn in the hope of heading off unrest, with promises of a further $400bn (£245bn) over the next four years for education, infrastructure and healthcare.

A spoof news item posted on the internet on Sunday said King Abdullah was also offering $150bn in cash to buy out Facebook (and presumably close it down) "in order to end the Arab revolt". Although the source of the story – LOL News – should have given a clue that it was just a joke, the tale was sufficiently plausible for the Saudi government to issue a straight-faced official denial.

Throwing money around is the customary way for oil-rich Gulf potentates to deal with a problem. That is not a long-term solution and, even as a palliative, all the signs suggest it is becoming less and less effective.

It may be enough to placate some disaffected Saudis, as in the past, but many others are saying money is not the issue: they want real change. The question is whether that message will get through to King Abdullah without mass protests on the streets.